Related papers: Formulating Discrete Probability Flow Through Opti…
Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
Intelligent Transportation Systems (ITS) are vital in modern traffic management and optimization, significantly enhancing traffic efficiency and safety. Recently, diffusion models have emerged as transformative tools for addressing complex…
Dilute granular flows are routinely described by collisional kinetic theory, but dense flows require a fundamentally different approach, due to long-lasting, many-body contacts. In the case of silo drainage, many continuum models have been…
Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
Training a diffusion model approximates a map from a data distribution $\rho$ to the optimal score function $s_t$ for that distribution. Can we differentiate this map? If we could, then we could predict how the score, and ultimately the…
Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to minimal length. In coordinate representation the flow probability density is presented as infinite series…
Let $A \subset \mathbb{R}^d$, $d\ge 2$, be a compact convex set and let $\mu = \varrho_0 dx$ be a probability measure on $A$ equivalent to the restriction of Lebesgue measure. Let $\nu = \varrho_1 dx$ be a probability measure on $B_r :=…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…